Tigonometric Identies problem.. help!

[andyc18]

I need hep verifying two trig identity problems

1. (cot-csc)^2 = (1-cos)/(1+cos)


2. sin2tan2/tan2-sin2 = 1

Any help?
Thanks in advance!

[Dr Transport]

The easiest way to prove trig identities is to express all of the quantites in terms of sines and cosines, then start rearranging from there......

[andyc18]

I have tried doing that many times ..still having no luck..

[James R]

Could you please write out your questions again, with the variables, and all bracketing correct?

There's no way to tell is, by sin2 you mean (sin x)² or sin 2x.

Also, in your second problem, do you mean

\frac{\sin^2 x \tan^2 x}{\tan^2 x} - \sin^2 x

or something else?

Notation is important.

[James R]

Here's a solution to the first problem:

(\cot x - \mbox{cosec} x)^2\\
= \left(\frac{\cos x}{\sin x} - \frac{1}{\sin x}\right)^2\\
= \frac{(\cos x - 1)(\cos x - 1)}{\sin^2 x}\\
= \frac{(\cos x - 1)(\cos x - 1)}{1 - \cos^2 x}\\
= \frac{(\cos x - 1)(\cos x - 1)}{(1 + \cos x)(1 - \cos x)}\\
= \frac{1 - \cos x}{1 + \cos x}